What ≰ means
The left side is not smaller than, and not equal to, the right.
Read a ≰ b as "a is not less than or equal to b". It denies the whole of a b at once: a is not below b, and a is not the same as b either. For everyday numbers that leaves only one possibility, so 7 ≰ 5 says exactly what 7 > 5 says.
Why keep a separate sign, then? Because ≰ points at the claim that failed. In a proof by contradiction a writer assumes x ≰ y, which keeps the reader's eye on the that is being tested; in a counterexample it records that the inequality someone hoped for does not hold.
The sign earns its keep where things are only partly ordered. Take sets compared by inclusion: {1, 2} ≰ {2, 3} is true, and so is {2, 3} ≰ {1, 2}, because neither set sits inside the other. Here ≰ cannot be rewritten as >; it means "not ", and the two sides may simply be incomparable. The same holds for vectors compared component by component, divisibility among positive whole numbers and many orderings studied in order theory, the branch of mathematics about such relations.
Read the slash as the word "not"
A stroke through a relation sign usually negates it.
≰ belongs to a family: for "not equal", for "not a member of", for "not less than", for "not greater than or equal to". Unicode builds ≰ as followed by a combining stroke, so a program that normalises text may silently swap one spelling for the other; both are the same character to a careful search. Fonts draw the stroke at different angles, from a steep slant to almost vertical, and all of them are correct.
Formal mathematical notation, used mainly in proofs, textbooks and lecture notes; rare in chat or ordinary prose.
In a partial order ≰ does not mean >: the two sides may be incomparable.
Part of the collection
What it means when someone sends it to you
4 readingsThe left number is bigger; it says the same as 7 > 5.
Don't confuse it with
4
Related characters
2
Combination ideas
3Worth knowing
- The < and > signs reached print in 1631, in a book published under the name of the English mathematician Thomas Harriot; Pierre Bouguer added the bar for in 1734.
- In a partial order ≰ and can both be true of the same pair at once, something that can never happen with ordinary numbers.
Questions people ask
3Is ≰ just another way of writing >?
For ordinary numbers, yes: 7 ≰ 5 and 7 > 5 say the same thing. For sets, vectors and other partly ordered things, no: ≰ only says "not ", and the two sides may be incomparable.
How do you say ≰ out loud?
"Not less than or equal to", or "is not at most". In a lecture you will also hear "a is not less than or equal to b" spelled out in full.
Why does ≰ show as a box or question mark?
The font lacks the character. Switch to a font that covers mathematical symbols, such as Cambria Math, rather than retyping it.
More like this
11
How to type or find ≰
- Also called
- nleq · not leq · negated less-than-or-equal
- Search it as
- not less than or equal · ≰ · crossed out less than or equal · negated inequality · not at most · math inequality symbol
- Shows up in
- Anything that takes text · its shape is whatever your font draws
≰\2270Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.